Chinese Annals of Mathematics, Series B

, Volume 32, Issue 2, pp 303–320 | Cite as

Sharp bounds for symmetric and asymmetric diophantine approximation

  • Cornelis KraaikampEmail author
  • Ionica Smeets


In 2004, Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number, expressed in bounds for both the previous and next approximation. The authors sharpen his results with a geometric method and give both sharp upper and lower bounds. The asymptotic frequencies that these bounds occur are also calculated.


Continued fractions Diophantine approximation Upper and lower bounds 

2000 MR Subject Classification

28D05 11K50 


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Copyright information

© Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.EWI, DIAMDelft University of Technology and Thomas Stieltjes Institute for MathematicsDelftNetherlands
  2. 2.Universiteit Leiden and Thomas Stieltjes Institute for MathematicsLeidenNetherlands

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